We are planning to migrate users from an on-premise exchange environment to a new O365 tenant. During this migration the usernames will change, so for me it seams logical to script this migration using powershell. However I can't seem to find any documentation on how to restore an on-prem mailbox to a O365 maibox using powershell. I did found some links regarding the 'Start-VBORestoreSession' cmdlet but those links point me to a 404 page not found. There is documentation on a 'Start-VBOExchangeItemRestoreSession' but this cmdlet is not available in my "Veeam Backup for Microsoft Office 365 PowerShell".

I am using "Veeam.Backup365_3.0.0.422".

Is there any documentation available on how to migrate on-prem users to O365?

would like to know what exactly you're looking for? Do you want to restore the soft deleted mailbox from Onpremise server as when you migrate the mailbox from Onpremise to Online then Mailboxes on Exchange On-premise server goes into soft deleted state. You can restore the mailbox from the soft deleted state.

or

you're looking for script to migrate the mailbox from Exchange OnPremise to Online, there are three way to migrate the mailbox to O365

Depending on your requirement you choose either of one and according to that you do further configuration as each Migration is divided into Phases.

Hence If you could help us the exact requirement then we can suggest the best